>>53331152A cult-like group which espouses the sanctity and superiority of humanity, showing extreme resistance to attempts to grant Pokemon rights and equality with humans.
They use a lot of current shillmons, Lucario, Gengar, Gardevoir, those sorts.
Things is, it's not humans in charge.
It's the Pokemon.
These particularly popular, established species which hold a far greater deal of sway than most others.
In their current position, they hold political and economic power far greater than most Pokemon - to the point of being considered near equals in quite a few matters. Through using their trainers as mouthpieces, or sheer talent some have excelled and become prominent, if secret figures in the human world, due to their uniquely privileged status among Pokemon.
Thing is, if Pokemon everywhere became equal, everything they have, all their advantages and privileges will be undone, set to nothing, as they become completely equal with all other Pokemon.
And, well, they can't be having that.
As to how you implement it?
Maybe a gym leader is revealed to just kind of be along for the ride; their ace Pokémon is the one who's in charge.
Maybe some characters have unique dialogue options if you have one of the aforementioned shillmons, or they voice their opinions on the superiority of the civilised mons against all others.